What are two consecutive numbers whose squares differ by 31

So 2 consecutive numbers are number that come right after each other so the numbers could be represented as x and x+1 where x represents an unknown umber

squares are the number times itself so

x time x and (x+1) times (x+1)

so therefor the difference is 31

obviously (x+1) times (x+1) is bigger than x times x so

x times x = (x+1) times (x+1) - 31

so you multiply to findn the answer

x times x=x^2

pemdas so multiply

(x+1) (x+1)

use distributive property which si a (b+c) = ab+ac so

(x+1) (x+1) = (x+1) (x) + (x+1) (1)

distribute again

(x+1) (x) = x^2+1x

(x+1) (1) = 1x+1

(x+1) (x+1) = x^2+1x+1x+1=x^2+2x+1

so we have

x^2=x^2+2x+1-31

add like terms

x^2=x^2+2x-30

subtract x^2 from both sides

x^2-x^2=x^2-x^2+2x-30

0=0+2x-30

0=2x-30

add 30 to both sides

30=2x

divide both sides by 2

15=x

subsitute

x+1 is second number

15+1=16

the numbers are 15 and 16

their squares are 225 and 256

the numbers are 15 and 16